When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 183 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 61 cubic inches

Answer:25

Step-by-step explanation:

The value which shows the true solution to the logarithmic equation solved below is 1.

Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

The given logarithmic equation is,

[tex]\log_2x+\log_2(x+7)=3[/tex]

Use the addition property of log in above expression.

[tex]\log_2[x\times(x+7)]=3[/tex]

Use the power rule property of log in above expression.

[tex][x\times(x+7)]=2^3\\x\times(x+7)=8\\x^2+7x-8=0[/tex]

Solve the quadratic equation with the help of split the middle term method,

[tex]x^2+8x-1x-8=0\\x(x+8)-1(x+8)=0\\(x+8)(x-1)=0\\x=-8,1[/tex]

Here, the two values of variable we get. One is positive and another is negative. As the logarithmic function is defined only for positive real number as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

Learn more about the domain and range of the function here;

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Answer:

1

Step-by-step explanation:

edge 2022

Answer:

−6x^2 −26x +60

Step-by-step explanation:

Simplify the equation.

Answer:

So, when you look at a graph. Where the line passes over the X-Axis, that is the X intercept. Where the line passes over the Y-Axis, that is the y intercept.

Step-by-step explanation:

I am not sure I understand the question with all the typos and potentially missing parts.

as I understand it, it will take her 4 hours to reach her destination when going 15 mph.

and the question is how long the trip will take, if she travels at 12 mph.

4 h × 15 m/h = 4 × 15 m = 60 miles

that is the distance of her trip.

when going slower, the distance is of course still the same, only the needed time changes :

x h × 12 m/h = 60 m

x × 12 m = 60 m

x = 60/12 = 5 hours

the trip would take her 5 hours to complete (instead of 4).

Answer:

13 hours

Step-by-step explanation:

567/9= 63 mile per hour

819/63 = 13

13 hours

Answer:

13 hours

Step-by-step explanation:

how long does she drive in one hour?

567/9=63

she drives 63mph

819/63=13

it will take her 13 hours to drive 819 miless

Answer:

C.) mAngleGLI = 2mAngleGLH

Step-by-step explanation:

This question was not properly written

Complete Question

Select all the pairs of equivalent expressions.

a. (4³)³ and 4³ ⋅ 4³

b. (3⁴)⁴ and 3⁸ ⋅ 3⁸

c. 6⁴ ⋅ 3⁴ and 18⁸

d. 4³ ⋅ 5³and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴ • 12².

a. 12^4

b. 12^18

c. 12^35

d. 12^216

3. Choose an equivalent expression for 10⁶ ÷ 10⁴.

a. 10^2

b. 10^3

c. 10^10

d. 10^24

4. Select all the expressions that are equivalent to 7⁸ • 7.

a. 7³• 7³

b. 7^18/7^9

c. (7³)³

d. 7⁴ + 7⁵

e. 7⁴ • 7⁵

5. Is this equation correct?

6³⋅ 7³= 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

B. Yes; 6³ • 7³is equal to (6 • 7 • 3) or (42 • 3).

C. No; 6³ • 7³ is equal to (6 • 7 • 3) or (42 • 3).

D. No; 6³ • 7³ is equal to (6 • 7)³+ 3 or 42⁶.

Answer:

1 The correct answer is

d. 4³ ⋅ 5³ and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2b. 12^18

3 a = 10²

4a. 7³ • 7³

c. (7³)³

e. 7⁴ • 7⁵

5 A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

Step-by-step explanation:

1) Select all the pairs of equivalent expressions.

These are the correct options

d. 4³ ⋅ 5³and 20³

4³ × 5³ = 8000

20³ = 8000

e. (43)3 and 43 ⋅ 43 ⋅ 43

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴• 12².

For an Algebraic Expressions,

We have the rule

x^a × x^b = x ^a+ b

Hence: 12³ • 12⁹• 12⁴ • 12².

= 12^3+9+4+2 = 12^18

Hence, b. 12^18

3. Choose an equivalent expression for

10⁶ ÷ 10⁴.

For an Algebraic expressions

x^a ÷ x^b = x ^a - b

Therefore

10⁶÷ 10⁴ = 10²

a. 10^2 Is the correct option

4. Select all the expressions that are equivalent to 7⁸ • 7.

7⁸ . 7= 7^8+1

= 7^9 or 7⁹

The equivalent expressions are:

a. 7³ • 7³ = 7⁹

b. 7^18/7^9 = 7⁹

c. (7³)³ = 7⁹

e. 7⁴ • 7⁵ = 7⁹

5. Is this equation correct?

6³ ⋅ 7³ = 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³

Answer:

x= 17/2 is the correct answer

Answer:

8 pizzas

Step-by-step explanation:

If each of the 20 people eats 3/8 of pizza, to calculate the total number of pizzas needed, multiply 20 by 3/8 and round up to the nearest whole number.

[tex]\sf total \ number \ of \ pizzas=20 \times\dfrac38[/tex]

                                  [tex]=\dfrac{20 \times3}8[/tex]

                                  [tex]=\dfrac{60}8[/tex]

                                  [tex]=\dfrac{15}2[/tex]

                                  [tex]=7.5[/tex]

Therefore, he should buy 8 pizzas for the party.

Answer:

polyester, orange

polyester, blue

polyester, yellow

cotton, orange

cotton, blue

cotton, yellow

Step-by-step explanation:

Answer:

51 inches

Step-by-step explanation:

I hope this helps!

51 inches tall is Kelly .

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

Kelly is 4 feet , 3 inches tall.

We know that,

1 foot = 12 inches

Convert the feet given to inches: 4 × 12 = 48

48 + 3 = 51 inch.

Hence, 51 inches tall is Kelly .

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The true solution to the logarithmic equation log(x)+log(x+5)=log(6x+12) is 4 option second is correct.

It is given the logarithmic equation [tex]\rm logx+log(x+5)=log(6x+12)[/tex].

It is required to find the true solution to the above logarithmic equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b=c\\[/tex]

[tex]\rm log_ac=b[/tex]

We have:

[tex]\rm logx+log(x+5)=log(6x+12)[/tex]

By using log property:

[tex]\rm logx + logy= log(xy)[/tex]

[tex]\rm log((x)(x+5))=log(6x+12)[/tex]

Taking [tex]\rm log_1_0[/tex] base and removing the log from the sides we get:

[tex]\rm x(x+5)= 6x+12\\\\\rm x^2+5x=6x+12\\\\\rm x^2-x-12=0[/tex]

It is quadratic equation solving by factorization method:

[tex]\rm x^2-x-12=0\\\\\rm x^2+3x-4x-12=0\\\\\rm x(x+3)-4(x+3)=0\\\\\rm (x+3)(x-4)=0\\\\\rm x+3=0 \ or \ x-4=0\\\\ \rm x=-3 \ or \ x=4\\\\[/tex]

A negative Logarithm value does not exist.

Hence, the true solution to the logarithmic equation log(x)+log(x+5)=log(6x+12) is x = 4

Learn more about the logarithm here:

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Consider the missing lines of question are "Due to the Enhanced Community Quarantine, Grand Royal Spa temporarily stopped its operation and to help the employees, the owner decided to split evenly its total revenue of 65,000.00".

Given:

Total revenue = 65000

Number of employees = x

To find:

The function which represents the  amount each received.

Solution:

We know that,

[tex]\text{Amount each received}=\dfrac{\text{Total revenue}}{\text{Number of employees}}[/tex]

Substitute the given values in the above formula.

[tex]\text{Amount each received}=\dfrac{65000}{x}[/tex]

So, the function which represents the  amount each received is

[tex]f(x)=\dfrac{65000}{x}[/tex]

Therefore, the required function is [tex]f(x)=\dfrac{65000}{x}[/tex].

Note: Given options are not correct and option C is incomplete.

Solution,

The population of a city is 2,549,786.

We can convert it into nearest million as follows :

Million = 10 lakhs

Rounding off to the nearest million

2,549,786 = 3,000,000

There are 6 zeroes after 3. We can express as the product of a single digit and a power of 10 as follows :

[tex]3,000,000=3\times 10^6[/tex]

Hence, the population of the city is 2,549,786 or [tex]3\times 10^6[/tex].

Answer: y=4.5, z=6.7, x=6

Step-by-step explanation:

Answer:

Frank is correct.

Step-by-step explanation:

Frank is correct because the bag does not have 49 marbles but it does have 7 total.

You can double check this: 6 + 1 =7. 7 marbles total so frank is correct!

Have an amazing day!!!

PLEASE RATE!!

Answer:

give me a sec........I need to analyze somethings

The equation for the first and second model will be y = - (x + 3)³ and y = 2(√x) + 1, respectively.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The equation for a cubic function that has been reflected over the x-axis and shifted left 3 units. Then add 3 in the function and multiply the function by negative 1.

y = - (x + 3)³

The equation for a square root function has been stretched by a factor of 2 and shifted 1 unit up. Then multiply the function by 2 and add 1 to the function.

y = 2(√x) + 1

More about the function link is given below.

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Answer:

The new points after a rotation of 180 degrees is;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

Step-by-step explanation:

Given a point (x , y) and we rotate by 180 degrees , the new point will be (-x , -y)

So to the question;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

9514 1404 393

Answer:

  9 cups

Step-by-step explanation:

If x represents the number of cups of dark chocolate needed for 60 candies, the proportion can be ...

  cups/candies = 3/20 = x/60

Multiplying by 60 gives ...

  x = 60(3/20) = 9

You need 9 cups of chocolate for 60 candies.

Answer:

[tex]P(Yellow\ or\ Green) = 0.524[/tex]

Step-by-step explanation:

Given

[tex]Yellow = 5\ seconds[/tex]

[tex]Green = 50\ seconds[/tex]

[tex]Red = 50\ seconds[/tex]

Required

Determine the probability of Green or Yellow

First, we need to determine the total time

[tex]Total = 50 + 50 + 5[/tex]

[tex]Total = 105\ seconds[/tex]

Next, is to determine the required probability

This is calculated as follows:

[tex]P(Yellow\ or\ Green) = P(Yellow) + P(Green)[/tex]

[tex]P(Yellow\ or\ Green) = \frac{n(Yellow)}{Total} + \frac{n(Green)}{Total}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{5}{105} + \frac{50}{105}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{5 + 50}{105}[/tex]

[tex]P(Yellow\ or\ Green) = \frac{55}{105}[/tex]

[tex]P(Yellow\ or\ Green) = 0.52380952381[/tex]

[tex]P(Yellow\ or\ Green) = 0.524[/tex] -- Approximated

Answer:

$12.33

Step-by-step explanation:

74/6 = 12.33

Answer:

12.3

Step-by-step explanation:

I hope this is right!

Answer:

y = 163°

Step-by-step explanation:

the angle with value 163° is actually an opposite angle of the angle y

Answer:

the angle is 163

Answer: try to find the triangle and then mesure it

Step-by-step explanation:

Answer:

∠x = 50°

Step-by-step explanation:

All external angles of a polygon add up to 360°.

Therefore,

Answer:

[tex]\sf \dfrac{27}{512}[/tex]

step:

[tex]\hookrightarrow \sf (\dfrac{3}{8} )^3[/tex]

rewrite:

[tex]\hookrightarrow \sf (\dfrac{3}{8} )(\dfrac{3}{8} )(\dfrac{3}{8} )[/tex]

remove parenthesis

[tex]\hookrightarrow \sf(\dfrac{9}{64} )(\dfrac{3}{8} )[/tex]

final answer

[tex]\hookrightarrow \sf \dfrac{27}{512}[/tex]